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scripts default iconARMAX-GARCH Toolbox (Estimation, Forecasting, Simulation and Value-at-Risk Applications) (Scripts) Publisher's description

ARMAX-GARCH Toolbox (Estimation, Forecasting, Simulation and Value-at-Risk Applications)

ARMAX-GARCH Toolbox (Estimation, Forecasting, Simulation and Value-at-Risk Applications)

The ARMAX-GARCH Toolbox estimates, forecasts and simulates a large variety of ARMA and GARCH models with different distributions and for any order of AR(n), MA(m), ARCH (p) and GARCH (q) effects as well as it allows any number of factors in the mean and volatility process. Furthermore, the Toolbox allows the evaluation of volatility forecasts using a number of loss functions and the estimation of Value-at-Risk for a given confidence level and horizon period. Finally, a number of examples are presented to illustrate the application of this toolbox in Market Risk and Financial Risk Management.

The supported models are:
GARCH, GJR-GARCH, EGARCH, NARCH (Nonlinear ARCH), NGARCH (Nonlinear GARCH), AGARCH (Asymmetric GARCH), APGARCH (Asymmetric Power GARCH), and NAGARCH (Nonlinear Asymmetric GARCH).

The supported distributions are:
Gaussian Normal, Student t, Generalized Error, Cauchy, Hansen’s Skew-t, and Gram-Charlier Expansion Series with constant higher-moments.

The main functions are:
1. garch.m, which estimates the ARMAX-GARCH family of models.
a. The function’s inputs are a data vector, the GARCH model to be estimated, the distribution of the innovation terms, the order of AR, MA, ARCH and GARCH effects as well as a vector of factors for the mean and volatility process.
b. The function’s outputs are a vector of estimated parameters, standard errors estimated by the inverse Hessian, the Log-Likelihood value, a vector of conditional variances, the residuals, and a summary of results which includes: model statistics, t-statistics, robust standard errors, scores among others.

2. garchfind.m, which finds the combination of models and distributions that better fits the data based on a set of criteria (i.e. largest log likelihood value and the smallest AIC and BIC criteria).

3. garchsim.m, which simulates GARCH responses given the model, distribution, number of samples and number of paths. Additionally, a vector of time series of positive pre-sample conditional standard deviations may be provided, which the variance model will initialize.

4. garchfor.m & garchfor2.m, which estimates mean and volatility forecasts given the model, distribution, and number of forecasts.

5. garchvar.m & garchvar2.m, which estimates Value-at-Risk for a given confidence level and horizon period for both long and short positions.

6. garchvolfor.m, which is an application in Volatility Forecasting & Value-at-Risk. It allows the comparison of volatility and Value-at-Risk estimates for a data vector and for a variety of GARCH models and distributions as specified in the model & distribution variables and at different forecast periods as well as sort the results according to only a sub-set of forecast periods.

Other features of garchvolfor function are:
6.1 The presentation of results (i.e. volatility loss functions and VaR back-testing) given by a sub-set of forecast periods. For example we may want to forecast volatility for upto to 22 days. In this case max_forecasts will equal 22, but we are only interested for the 1-day, 1- and 2-weeks and 1-month trading periods and therefore we specify int_forecasts as [1, 5, 10, 22].

6.2 Organization of results based either by model or by series names. Important feature in case we have a number of different indices and models where we can quickly organize the results in the format we prefer.

6.3 Plotting of the volatility and VaR forecasts by adjusting the fields in the options variables which include series names, time steps, size of plots and a path where the plots are to be saved.

6.4 With the help of the VFLF and VaRLR functions a number of volatility loss functions and the VaR unconditional, independence, conditional and regulatory tests are also estimated. The volatility loss functions are the following: MSE; MAD; MLAE; HMSE; HMAE; MAE; MAPE; R2LOG; QLIKE; SR. The VaR back-testing tests are: percentage of failures, TUFF; Likelihood Ratio Unconditional Coverage, Independence Coverage, and Conditional Coverage; Basel II Accord, Basel.

For more information which tests are included please refer the VFLF and VaRLR functions.

For further information regarding the full functionality and a set of examples of the ARMAX-GARCH Toolbox please refer to the readme files.

Additional files for garchvar and garchvolfor can be found in:

I would like to thank you for your comments and your suggestions regarding additional features that should be included.

Please feel free to contact me with comments, suggestions, or bugfixes.

System Requirements:

MATLAB 7.11 (2010b)
Program Release Status: New Release
Program Install Support: Install and Uninstall

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